A continuum theory describing the behaviour of dielectric materials containing mobile, electrically charged vacancies was formulated. The theory was implemented to simulate diffusion, at the nanometer scale, of oxygen vacancies in acceptor-doped barium strontium titanate thin films in the para-electric state. In the simulations, charged vacancies coalesce into boundary layers of large concentration at potential-free interfaces, with increases in the local electric field intensity emerging near such boundaries. Upon relating this increase to a reduction in the energy barrier for charge transmission from film to electrode at the interface, and accepting an inverse relationship between the concentrations of doping elements and mobile oxygen vacancies, the model shows agreement with observed trends of decreasing current losses with increased doping.

Continuum Modelling of Charged Vacancy Migration in Elastic Dielectric Solids, with Application to Perovskite Thin Films. J.D.Clayton, P.W.Chung, M.A.Grinfeld, W.D.Nothwang: Mechanics Research Communications, 2008, 35[1-2], 57-64